According to Durr-e-Mukhtaar the six fasts of Shawwaal may be incorporated with Qadhaa fasts (to acquire their thawaab as well). But this is incorrect. Tadaakhul (or incorporation of two different acts of ibaadat) will be proper if the purpose of both could be achieved by the incorporation, e.g. Tahayatul Musjid. It’s object is to discharge the right (haqq) of the Musjid by performing Salaat immediately on entering. Hence if a person engages in Sunnat Salaat on entering, the objective of Tahayatul Musjid will also be simultaneously acquired. Thus, tadakhul will be correct in this case. On the contrary, tadakhul will not serve to attain the purpose of the six fasts of Shawwaal.
Explaining the objective of these six fasts, the Hadith Shareef says: “The fasting of the month (of Ramadhaan) equals ten months (of fasting), and the six days (of Shawwaal) equals two months. Thus, this is the full year (12 months).” (Narrated by Daarami)
Another Hadith states: “Whoever renders a good act, for him will be (thawaab equal) to ten times the act.” (Ibn Maaj’ah) This full year of fasting (i.e. its thawaab) is possible only if in addition to Ramadhaan, six days are fasted in Shawwaal.
[Malfoozaat Hakeemul Ummat]